A further improved (G′/G)- expansion method and the extended tanh- method for finding exact solutions of nonlinear PDEs

Abstract

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the (1 + 1) dimensional modified Kawahara equation by using the following two methods: (i) A further improved (G′/G)- expansion method, where G = G(ξ) satisfies the auxiliary ordinary differential equation [G′(ξ)]2 = aG2(ξ) + bG4(ξ) + cG6(ξ), where ξ = x - Vt while a, b, c and V are constants. (ii) The well known extended tanh- function method. We show that the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before.